There are two things about this book that aren't grabbing me, but I think they spring from the same well.
The first is the little inconsistencies. Grif drops his cigarette when he sees Anne, but a few sentences later he takes a drag on it. Did he pick it off the street and put it back in his mouth? Light another one? It throws me.
The smoking itself feels like the author doesn't know what to have the characters do in terms of body language, so she goes for the same filler stuff each time, which is why it isn't consistent. It's tacked on.
The Rockabilly stuff feels equally tacked on. Not integral, but painted into a scene here or there, more like frosting than an ingredient that got baked into the story. So it reads false.
It is a good story, don't get me wrong, but those moments are spell breakers.
That said, I will continue reading this series when the next book comes out. It's just compelling enough.